An annoyed teacher asked her student to do the following:
(1) Start with the number 12. Go to step (2).
(2) Take the negative of the number reached at the end of the previous step. Go to step (3).
(3) Add 1 to the number reached at the end of the previous step. Go to step (4).
(4) Go back to step (2) unless you have already gone through step (3) a hundred times; if you have gone through step (3) a hundred times already, tell the teacher the last number you reached.
To the teacher's surprise, the student gave her the correct final answer within a minute. What was it?
-1 * 12 = -12
-12 + 1 = -11
-1 * -11 = 11
11 + 1 = 12
After the second attempt of the process, you reach the number given in the problem in the very beginning. What does that mean? If you continue doing these 2 steps, 12 is the result of an even number of attempts, correct? Try it. Do it for a fourth, sixth, and eigth attempt and I guarantee you will reach 12. If we call the two attempts a process, do the process 50 times and that is a 100th attempt and that must mean that you will reach 12.